A recursive method to find the extreme and superstable curves in the parameter space of dissipative one-dimensional mappings

Autor(es)

da Costa, Diogo Ricardo ; de Paiva, Luam Silva ; Rocha, Julia G. S. ; Hermes, Joelson D. V. ; Hansen, Matheus ; Viana, Ricardo Luiz ; Caldas, Ibere Luiz ; Medrano-T, Rene O.

• Tipo de documento: Artigo Científico
• Fonte: Chaos; v. 35, n. 2, p. 11-pg., 2025-02-01.

Resumo

This paper presents a recursive method for identifying extreme and superstable curves in the parameter space of dissipative one-dimensional maps. The method begins by constructing an Archimedean spiral with a constant arc length. Subsequently, it identifies extreme and superstable curves by calculating an observable psi. The spiral is used to locate a region where psi changes sign. When this occurs, a bisection method is applied to determine the first point on the desired superstable or extreme curve. Once the initial direction is established, the recursive method identifies subsequent points using an additional bisection method, iterating the process until the stopping conditions are met. The logistic-Gauss map demonstrates each step of the method, as it exhibits a wide variety of periodicity structures in the parameter space, including cyclic extreme and superstable curves, which contribute to the formation of period-adding structures. Examples of extreme and superstable curves obtained by the recursive method are presented. It is important to note that the proposed method is generalizable and can be adapted to any one-dimensional map. (AU)

• Processo FAPESP: 20/02415-7 - StatGraph 2.0 e um massivo curso online gratuito (MOOC)
• Beneficiário: Diogo Ricardo da Costa
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 24/06718-5 - Bacias de Atração: De mapas unidimensionais a redes complexas
• Beneficiário: Rene Orlando Medrano Torricos
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 19/09150-1 - Efeito de tempo de atraso e plasticidade em sincronização neuronal
• Beneficiário: Matheus Hansen Francisco
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 18/03211-6 - Dinâmica não linear
• Beneficiário: Iberê Luiz Caldas
• Modalidade de apoio: Auxílio à Pesquisa - Temático